In probability theory and statistics, exponential distribution describes the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. The situations in which exponential distribution appears to be the most natural have as an essential feature the random recurrence (often in time) of an event. These include, for example, experiments on radioactive decay, telephone call arrivals, and insurance mathematics.

Characterizations are particularly of interest when they shed light on the consequences of certain distributional assumptions and can be used in goodness-of-fit tests which, in turn, can lead to an acceptable model. We will present certain generalizations of Arnold and Villasenor’s [1] exponential characterizations. Part of the results in this talk appeared in Yanev and Chakraborty [2]. ­­We will also discuss some open problems.